Horst Seehofer and Angela Merkel at a parliamentary group meeting on Tuesday.
Photograph: Clemens Bilan/EPA

Angela Merkel has come under under intense pressure to tighten Germany’s refugee policies or risk the collapse of her coalition government as an increasingly urgent argument over how to handle irregular migration rattles Europe.

While the standoff between the chancellor and her interior minister, Horst Seehofer, continued on Thursday, the French president, Emmanuel Macron, and Italy’s new prime minister, Giuseppe Conte, said they would discuss “new initiatives” on immigration this week in Paris.

A day after the Austrian chancellor, Sebastian Kurz, called on an “axis of the willing” to tackle the EU’s migration impasse, Pope Francis also weighed in to the debate, demanding more international cooperation on refugees and a “change of mindset” from politicians everywhere.

Merkel and Seehofer spoke for two-and-a-half hours on Wednesday night without reaching agreement on the hardline interior minister’s demand that refugees who arrive at Germany’s borders should be turned back.

The chancellor is said to have urged Seehofer to wait until a 28 June EU summit at which she would seek a Europe-wide agreement. But Seehofer reportedly told her the EU had failed to forge a common policy since the refugee crisis erupted in 2015 and it was hardly credible to think it would do so by the end of the month.

A Bundestag session was interrupted for two hours on Thursday morning so Merkel’s Christian Democrats (CDU) and their Bavarian sister party the CSU, to which Seehofer belongs, could hold separate emergency meetings.

Merkel, the EU’s longest-serving leader, on Wednesday called immigration “a litmus test for Europe” requiring “a truly unified approach”, but amid signs that support for her within the CDU is dwindling on the issue, it has also become a flashpoint for mounting tensions within her own conservative bloc.

Italy and France, meanwhile, sought to patch up a worsening diplomatic row over the same question, triggered by Macron’s description of a decision by the Italian interior minister, Matteo Salvini, to deny a migrant rescue ship access to Italy’s ports as “an act of cynicism and irresponsibility”.

Rome summoned France’s ambassador on Wednesday and Salvini, leader of the far-right League party, demanded an apology, but the Elysée palace said on Thursday the French president had “not made any comment intended to offend Italy or the Italian people” and that Paris sought “constructive dialogue”.

The row centred on the Aquarius, now on its way to Valencia in Spain with 629 migrants rescued off the coast of Libya last week. The ship, operated by the charity SOS Méditerranée, was turned away by both Italy and Malta.

Salvini insisted on Thursday that ships “belonging to foreign organisations and flying foreign flags will not be allowed to dictate Italy’s immigration policy”.

More than 1.8 million migrants have arrived in Europe since 2014 and Italy is currently sheltering 170,000 asylum seekers and an estimated 500,000 unregistered migrants. More than 1 million migrants arrived in Germany in the summer of 2015 after Merkel opened the country’s borders.

The June summit in Brussels is due to discuss proposals to change the bloc’s asylum laws, which currently require refugees to apply for asylum in the first EU country they enter, generally Italy or Greece.

But the bloc is bitterly divided over how to share the burden between southern “frontline” states, northern “destination” countries, and hardline central and east European governments like Hungary and Poland which want nothing to do with any compulsory quota system.

In an interview with the Guardian, Spain’s foreign minister, Josep Borrell, a former president of the European parliament, said Europe had to find agreement over the way to take in asylum seekers. “The approach of people asking for asylum in the first country they reach is now manifestly an obsolete rule that doesn’t work.”

Borell warned that because people often do not want to stay in the country they first arrive in, “unless we can find a solution to these problems, Europe’s Schengen system that will collapse”.

Speaking at a migration conference at the Vatican, Pope Francis urged countries to work together and “move from considering others as threats to our comfort to valuing them as persons ... who can contribute greatly to the enrichment of our society”.

Party leaders believe the CSU needs to be firm on the emotive immigration issue, opening a potentially damaging rift with Merkel’s CDU and provoking the worst crisis of the veteran chancellor’s fourth-term coalition, which took more than six months to build after inconclusive elections last year.

The interior minister’s main demand is that asylum seekers be turned back at the German border if they entered the EU in another country, or have already applied for asylum in Germany and had their applications turned down.

Merkel has said it would be illegal for Germany to take such a unilateral step, which would damage attempts to shape a comprehensive EU policy, but reportedly offered a compromise, proposing bilateral agreements with Italy and Greece.

Merkel and Seehofer have been increasingly at loggerheads over the refugee issue. Political observers say Merkel may rue the day she gave the nod to Seehofer’s appointment as interior minister.

Seehofer’s decision to back out of attending an integration summit in Berlin on Wednesday only increased the tension. He went instead to meet Kurz, after which the two announced a three-way “axis of the willing” between Austria, Germany and Italy to fight illegal immigration.

The move was seen as a deliberate shunning of Merkel and an outright rejection of her ideas on migration policy. According to polls, 65% of Germans reject Merkel’s stance on migration and would like to see tighter controls at Germany’s borders.